Admissible heuristics for automated planning by by Patrik Haslum.

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Time line values are ascribed meaning by constraints, which describe the valid transitions between values on each time line and dependencies between values on different time lines (this use of constraints to describe the planning problem is not the same as the use of constraints and CSP techniques to represent and reason with search states, which has been applied also in planning systems using temporal STRIPS or similar models). A planning problem is specified by a partial description of the set of time lines, consisting of assertions about the values held by variables over intervals of time, and the task of the planner is to complement this description with additional assertions and further constrain the assertion intervals, until all constraints of the problem are satisfied.

A planning problem is specified by a partial description of the set of time lines, consisting of assertions about the values held by variables over intervals of time, and the task of the planner is to complement this description with additional assertions and further constrain the assertion intervals, until all constraints of the problem are satisfied. p)), while the fact that the UAV is flying along a path between two positions is represented by an action. p1). p1. p0. , initially and at the end of the plan, the UAV is on the ground at point p0, but for some interval (of at least 20 seconds) in between, it should be hovering at the observation point p42.

Since s ⊆ s, a is applicable in s and thus hm (s) m h ((s −del(a))∪pre(a))+cost(a). Since (s −del(a))∪pre(a) ⊆ (s−del(a))∪pre(a), hm ((s −del(a))∪pre(a))+cost(a) hm ((s−del(a))∪pre(a))+cost(a), contradicting the assumption. ✷ The Generalized Bellman-Ford Algorithm The Generalized Bellman-Ford (GBF) algorithm is a “label correcting” algorithm: it assigns a crude initial cost estimate to every state and then iteratively applies local updates until costs converge. g. Cormen, Leiserson, & Rivest, 1990) to graphs with directed multi-edges.

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